求解有界约束二次规划问题神经网络模型的收敛性分析  

Convergence Analysis of a Neural Network for Quadratic Optimization with Bound Constraints

作　　者：李有梅[1] 彭济根[1] 徐宗本[1] 

机构地区：[1]西安交通大学理学院信息与系统科学研究所

出　　处：《系统工程理论与实践》2003年第9期98-104,128,共8页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(69975016)

摘　　要：　通过深化Lasalle不变原理,建立了判别一般动力系统全局收敛性的一个准则.应用这一准则,详尽研究了一个求解有界约束二次规划问题神经网络的全局收敛性,给出了当目标函数为一类非凸函数时的全局收敛性条件.特别地利用常微分方程理论,证明了该网络对任意凸函数全局收敛性,所获结果深化和推广了现有文献相关结论的相应结论.这些新的结论都表明了该神经网络在求解有界约束二次规划问题时的有效性.数值模拟与理论分析结果一致.In this paper, we present a general principle by sharpening lasalle invariance principle to judge the convergence of a dynamic system. Based on this, The global convergence of a neural network for quadratic optimization with bound constraints is studied in detail,and some new conditions are obtained on which the neural network can be guaranteed to be globally convergent for a non\|convex objective function. Specially using ordinary differential equation theory, the global convergence of the neural network is proved when objective function is convex, this conclusion generalizes and deepens the corresponding results obtained in current literaturess. All these new results show the validity of the network in solving quadratic optimization with bound constraints. Finally, two numerical examples are given to demonstrate the correctness of the theoretical results.

关 键 词：神经网络 二次优化 全局收敛 平衡点 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]